Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge Theories
We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables the efficien...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-10-01
|
| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.4.040317 |
| _version_ | 1797648799067275264 |
|---|---|
| author | Poetri Sonya Tarabunga Emanuele Tirrito Titas Chanda Marcello Dalmonte |
| author_facet | Poetri Sonya Tarabunga Emanuele Tirrito Titas Chanda Marcello Dalmonte |
| author_sort | Poetri Sonya Tarabunga |
| collection | DOAJ |
| description | We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables the efficient extraction of the magic contained in the correlations between widely separated subsystems, which characterizes the nonlocality of magic. Our method can be implemented in a variety of situations. We describe an efficient sampling procedure using tree tensor networks, that exploit their hierarchical structure leading to a modest O(logN) computational scaling with system size. To showcase the applicability and efficiency of our method, we demonstrate the importance of magic in many-body systems via the following discoveries: (a) for one-dimensional systems, we show that long-range magic displays strong signatures of conformal quantum criticality (Ising, Potts, and Gaussian), overcoming the limitations of full state magic; (b) in two-dimensional Z_{2} lattice gauge theories, we provide conclusive evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes. Finally, we discuss an experimental implementation of the method, which relies only on measurements of Pauli observables. |
| first_indexed | 2024-03-11T15:37:14Z |
| format | Article |
| id | doaj.art-67a19df361ad407894b93b1204d89fc1 |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-03-11T15:37:14Z |
| publishDate | 2023-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-67a19df361ad407894b93b1204d89fc12023-10-26T15:06:43ZengAmerican Physical SocietyPRX Quantum2691-33992023-10-014404031710.1103/PRXQuantum.4.040317Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge TheoriesPoetri Sonya TarabungaEmanuele TirritoTitas ChandaMarcello DalmonteWe introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables the efficient extraction of the magic contained in the correlations between widely separated subsystems, which characterizes the nonlocality of magic. Our method can be implemented in a variety of situations. We describe an efficient sampling procedure using tree tensor networks, that exploit their hierarchical structure leading to a modest O(logN) computational scaling with system size. To showcase the applicability and efficiency of our method, we demonstrate the importance of magic in many-body systems via the following discoveries: (a) for one-dimensional systems, we show that long-range magic displays strong signatures of conformal quantum criticality (Ising, Potts, and Gaussian), overcoming the limitations of full state magic; (b) in two-dimensional Z_{2} lattice gauge theories, we provide conclusive evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes. Finally, we discuss an experimental implementation of the method, which relies only on measurements of Pauli observables.http://doi.org/10.1103/PRXQuantum.4.040317 |
| spellingShingle | Poetri Sonya Tarabunga Emanuele Tirrito Titas Chanda Marcello Dalmonte Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge Theories PRX Quantum |
| title | Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge Theories |
| title_full | Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge Theories |
| title_fullStr | Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge Theories |
| title_full_unstemmed | Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge Theories |
| title_short | Many-Body Magic Via Pauli-Markov Chains—From Criticality to Gauge Theories |
| title_sort | many body magic via pauli markov chains from criticality to gauge theories |
| url | http://doi.org/10.1103/PRXQuantum.4.040317 |
| work_keys_str_mv | AT poetrisonyatarabunga manybodymagicviapaulimarkovchainsfromcriticalitytogaugetheories AT emanueletirrito manybodymagicviapaulimarkovchainsfromcriticalitytogaugetheories AT titaschanda manybodymagicviapaulimarkovchainsfromcriticalitytogaugetheories AT marcellodalmonte manybodymagicviapaulimarkovchainsfromcriticalitytogaugetheories |